Distributing negative signs in logarithms

[RChristenk]

Homework Statement

Simplify $\log(A \times B \div C \times D)$

Relevant Equations

Logarithm Rules

Simplify $\log(A \times B \div C \times D)$

Is it $\log(A)+\log(B)-(\log(C)+\log(D))$ or $\log(A)+\log(B)-\log(C)+\log(D)$?

I'm leaning toward the former but not sure. Thanks.

 

[Frabjous]

It depends on whether the statement means
$log[\frac {ab} {cd}]$ or $log[\frac {abd} {c}]$
Normal convention says the latter so log(a)+log(b)-log(c)+log(d)

 

[Mark44]

Simplify $\log(A \times B \div C \times D)$

I have not seen any algebra textbooks that would show problems like this. As already noted, the expression in parentheses should be written as either $\frac{AB}C \cdot D$ or as $\frac{AB}{CD}$. Failing that, there should at least be parentheses around CD to emphasize that this is the divisor.
Is this a problem from some textbook? If so, my guess is that it is substandard or very old.
Also, algebra textbooks generally don't use the $\div$ sign.